Crystals thickness

The thickness depends on the supercooling, which, in turn, is the result of kinetic considerations. Accordingly, crystal thickness is related to T, but neither have much to do with T . 

Figure 4.5 Crystal thickness versus Tjj,/AT for polyethylene. (Reprinted with permission from Ref. 5, copyright 1964, McGraw-Hill.)...

Andrew Keller (1925-1999) who in 1957 found that the polymer polyethylene, in unbranched form, could be crystallised from solution, and at once recognised that the length of the average polymer molecule was much greater than the observed crystal thickness. He concluded that the polymer chains must fold back upon themselves, and because others refused to accept this plain necessity, Keller unwittingly launched one of the most bitter battles in the history of materials science. This is further treated in Chapter 8, Section 8.4.2. 

We now discuss the effects of finite chain length. The difficulties arise from the definition of a bulk free energy term, when the very nature of the chains constrains the crystal thickness to be finite. There are two different approaches to this problem the first to be considered is due to Hoffman et al. [31] and is a simple modification of the infinite chain case, but is somewhat lacking in theoretical justification the second, due to Buckley and Kovacs [23], aims to correct this deficiency and suggests that the interpretation of experimental data given by Hoffman s approach is misleading. 

We now turn to obtaining estimates for the expected crystal thickness, that is the solution of Eq. (3.97), for various values of C, where C, = 0 for / < lmi and increases with l otherwise. The case C, = constant can be used to show that the finite probability of folding is sufficient to obtain a finite thickness at all supercoolings thus avoiding the SI catastrophe, which was demonstrated in Sect. 3.7.1. This case is unphysical and was only considered because of its mathematical simplicity. It leads to the prediction that the thickness, though finite, increases with AT. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

Fig. 10. Linear plot of crystal hardness as a function of square root of crystal thickness for various metarials Paraffins (O) PE (M = 170.000) (A) PE (M, = 2x 106) ( )...

In comparing the correlation sought between MH and E one should emphasize the following while the plastic deformation of lamellae at larger strains when measuring MH depends primarily on crystal thickness and perfection in case of the elastic modulus the major role is played by the amorphous layer reinforced by tie molecules, which is elastically deformed at small strains. Figure 17 illustrates de... 

From the foregoing it is clear that indentation anisotropy is a consequence of high molecular orientation within highly oriented fibrils and microfibrils coupled with a preferential local elastic recovery of these rigid structures. We wish to show next that the influence of crystal thickness on AMH is negligible. The latter quantity is independent on 1 and is only correlated to the number of tie molecules and inter-crystalline bridges of the oriented molecular network. 

Annealing drawn PE hydrostatically at high pressure, generates a wide spectrum of crystal thicknesses varying from the common oriented chain folded to the chain-extended structures — where folds and ties tend to disappear63 —. This range of crystal thicknesses coupled with the chain axis orientation, offers a suitable model in... 

Daue Photographic Data prom Molybdenite Incident beam 8° 20 from normal to (0001). Crystal thickness 0.23 mm. 

Figure 2. Calculated CBED rocking curves for Si[ 110], a primary beam energy of 193.35 keV and a crystal thickness of 369nm. The three curves shown in the figure were calculated using 80 Bloch waves (circle+solid line) 20 Bloch waves (star solid line) and 5 Bloch waves (dotted line) and the curves correspond to the line of Figure 1 along A-D.

Figure 4. Calculated CBED rocking curves within the (000) and the (ill) disks in a Si[l 10] zone axis CBED pattern. All curves shown in the figure were calculated for a crystal thickness of 250 nm, and a primary beam energy of 196.35 keV., and correspond to the line scan A-B of Figure 1.

Figure 5. Calculated CBED rocking curves. This figure is essentially the same as Figure 4, except that all calculations were made for a crystal thickness of 500 nm.

Figure 9. Energy-filtered experimental and fitted Si[l 10] CBED rocking curves for (a) a line scan along the [111] direction and (b) a line scan along the [002] direction (see Figure 1). The calculations were made for a primary beam energy of 195.35keV and a crystal thickness of 369 nm.

The crystalline lamellar thickness Dc obtained by StrobPs method is initially 1.4 nm and grows to about 2.0 nm, which is roughly equal to the crystallite size in the chain direction of 2.8 nm estimated from the wide-angle X-ray diffraction (WAXD) [7]. Interestingly, the persistence length /p = 1.45 nm just before crystallization measured by SANS (also see Fig. 11) [9,10] is almost equal to the crystal thickness. 

Fig. 2 (a) Edwards E308 evaporator. One quartz-crystal thickness monitor is pointed towards the Au source to monitor Au vapor deposition on chamber walls the other monitors Au deposited through the shadow mask atop the organic layer. In the cold Au deposition, a small amount of Ar gas is added to the chamber to cool the Au atoms to room temperature before they physisorb atop the cryocooled organic monolayer, (b) Geometry of an Au I monolayer I Au pad sandwich, with electrical connections made using a Ga/In eutectic... 

Ellipsometry and profilometry Thickness, refractive index, and consolidation behavior during drying and crystallization. Thickness uniformity. 

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